In a number of disparate technical fields, there has been a constant effort to find improved methods of detecting subsurface objects such as tumours in the human body or land mines underneath the Earth's surface. These methods, known as electrical impedance tomography (EIT), are based upon imaging electrical conductivity or admittivity distributions within a body and generating an image of the subsurface objects based on these electrical conductivity or admittivity values. (The terms “conductivity” and “admittivity” are used interchangeably in the following and it is understood that these terms are the inverses, respectively, of “resistivity” and “specific impedance” or “impedivity”).
In biomedical imaging, it is also known that the human body has significant contrasts in electrical conductivity and permittivity (see “Compilation of the Dielectric Properties of Body Tissues at the RF and Microwave Frequencies” by C. Gabriel and S. Gabriel, Technical Report for AFOSR/NL Bolling AFB DC 20332-00014, December 1994-95) and that significant differences exist between biological materials. In cases where the conductivities between materials are similar, the relative permittivities are not and so images can be made to be distinct. Table 1 shows the conductivity and relative permittivity of biological tissues at frequencies of 10 kHz and 100 kHz.
TABLE 1Conductivity and relative permittivity of biologicaltissues at frequencies of 10 kHz and 100 kHzConductivityRelativeTissueFrequency(S/m)PermittivityLiver10kHz0.155.5 × 104Spleen100kHz0.620.326 × 104 Lung10kHz0.112.5 × 104Kidney100kHz0.251.09-1.25 × 104   Bone10kHz0.0130.064 × 104 Whole Blood100kHz0.550.40 × 104 Skeletal Muscle10kHz0.558.0 × 104
One such EIT methodology is disclosed in U.S. Pat. No. 4,539,640 issued to B. Fry and A. Wexler and in a publication by A. Wexler, B. Fry and M. R., Neuman, 1985, “Impedance Computed Tomography. Algorithm and System, “Applied Optics, Vol. 24, No. 23, pp. 3985-3992. The methodology taught by Fry et al. involves the injection of a plurality of electrical signals into a body in time sequence or as multiplex signals through input sites located either upon the surface of the structure or internally thereof, thereby causing current flow along a plurality of paths through each region of the body, which paths terminate in output sites located upon or within the body. At least one characteristic of each signal, such as amplitude, phase or waveform, is measured at a plurality of locations, which are sufficiently removed from the input and output sites. The measured characteristics are compared with the corresponding characteristics of the signal measured at one or more reference points upon or within the structure and the comparison signals obtained are utilized to mathematically reconstruct the spatial relationships between the regions within the structure. An image of the structure interior is then derived from the reconstruction of the aforesaid spatial relationships.
In Fry et al., there is no attempt to restrict the current flow. Rather, the current paths spread and the currents flow throughout substantially the entire region of interest. This general and unrestricted flow of current creates a voltage distribution pattern over the surface or within the region of interest, that may be measured at all sites over or within such region and not just at those active sites through which current is impressed or withdrawn. This surface voltage distribution is a function of the admittivity distribution of the body.
As is known in the art, it is inadvisable to measure voltages at electrodes that are at that moment actively injecting or extracting currents. Such voltage measurements will be influenced by uncertain voltage changes due to uncertain contact resistances. Because there are a large number of voltage measurement sites available that furnish information relative to the interior of the structure, there is little cost in dispensing with the very few, inaccurate voltage measurements taken at current input and output sites. Further, if voltage measurements are taken at high-impedance sites, negligibly small currents are drawn at such sites and, as a consequence, the problem of contact impedance voltage drop is largely avoided because of the solution of the field equations within the three-dimensional region.
The above is a generalization of the four-probe technique disclosed in “Some Observations Concerning Electrical Measurements in Anisotropic Media, and their Interpretation” by Schlumberger, C. and M., and Leonardon, Trans. AIME, Vol. 110, 1934, pg. 159; “Electrical Coring; a Method of Determining Bottom-Hole Data by Electrical Measurements” by Schlumberger, C. and M., and Leonardon, Trans. AIME, Vol. 110, 1934, pg. 237; and “A New Contribution to Subsurface Studies by Means of Electrical Measurements in Drill Holes” by Schlumberger, C. and M., and Leonardon, Trans. AIME, Vol. 110, 1934 pg. 273. Another description of the four-probe technique is described in “Applied Geophysics” by W. M. Telford, L. P. Geldart, R. E. Sheriff and D. A. Keys, Cambridge University Press: London, 1976.
The inclusion of extra equations, resulting from voltage measurements at high-impedance contact sites, permits a reduction in the number of excitations needed for equivalent image quality. This, therefore, reduces the number of computationally costly, three-dimensional field solutions. As a result, the image recovery process is speeded up.
The inverse problem associated with a single excitation configuration, that is the problem of reconstructing from the measured data an image representing the nonuniform distribution of conductivity over a body segment, may not have a unique solution. That is to say, there may be many internal structures that will produce the measured and observed voltage distribution. To reduce the indeterminacy it is necessary to impress a sequence of current-excitation patterns, one pattern at a time or in parallel, for example, by frequency multiplexing. The voltage field distribution is mapped for each case. If sufficient cases are tested, the uncertainty resolves itself to the state where the resultant “pictures” are left with a fuzzy outline. Increasing the number of measurements will improve the “focus” (following the photographic analogy). The measurements are made automatically, for example, using signal-averaging procedures. The data is then stored for subsequent computer analysis.
Fry et al. teaches that given a set of input signals, a computer may be used to “develop” an image of the body and the object located within the body. This is done by finding an internal conductivity distribution within the three-dimensional body that best satisfies, in an average sense, the plurality of measured voltage distribution patterns that result from the sequence of current-excitation patterns, in an iterative fashion. To do the analysis efficiently, a numerical method, such as the finite-difference or finite-element method is used, to produce an efficient solution to the resulting very large systems of equations.
The problem with the methodology disclosed in the Fry et al. patent and the Wexler et al. (1985) publication is that it requires a large number of field and conductivity iterations to generate the conductivity image pattern through a solution to the system of field equations that simultaneously satisfy all of the boundary conditions. Hence, this renders the methodology computationally inefficient.
Since their publication, several attempts have addressed the problem of computational inefficiency in the methodology disclosed in the Fry et al. patent and the Wexler et al. (1985) publication by using methods to accelerate the evolution of the conductivity image pattern. For example, U.S. Pat. No. 6,201,990 issued to A. Wexler and Z. Mu and U.S. Pat. No. 6,745,070 issued to A. Wexler, Z. Mu, R. M. Murugan and G. S. Strobel (collectively referred to below as the Wexler et al. patents) disclose several methods for accelerating the evolution of the conductivity image pattern, such as peak-detection, multi-step extrapolation and successive overrelaxation.
While these methodologies have achieved a significant reduction in the number of iterations for image recovery, the speed and accuracy for the imaging can be further improved using the methodology of the present invention. The reconstruction of images in a rapid manner is required for fast location and identification of very small objects in a body. The present invention provides an improved methodology, over that disclosed in the Fry et al. and the Wexler et al. patents, which is capable of imaging very small subsurface objects significantly faster than the methods of the prior art while producing an accurate image devoid of spurious effects.